The Hausdorff derivative of a linear order can be iterated to an ordinal length, giving a sequence of quotient linear orders, where each step requires a double jump to calculate.. Ash and Watnick give a converse to this, where the antiderivatives are product orderings of an appropriate lower complexity than the original ordering. Motivated by uncountable computability theory, we wanted a variant of this in which the derivatives are substructures rather than quotient structures. Once we had this, it turned out to apply not just to linear orders, but also graphs, trees and forests. I will explain our theorem primarily in the context of countable graphs and computability theory, but with some asides about other structures and uncountable computability theory.